Algebra 2/Trigonometry Regents Exam 0115Page 1

Algebra 2/Trigonometry Regents Exam 0115Page 1

1In , , , and . Which statement can be used to determine the numerical value of h?

1) /
2) /
3) /
4) /

2The table of values below can be modeled by which equation?

1) /
2) /
3) /
4) /

3The equation where and is equivalent to

1) /
2) /
3) /
4) /

4Which expression is equivalent to the sum of the sequence ?

1) /
2) /
3) /
4) /

5An investment is earning 5% interest compounded quarterly. The equation represents the total amount of money, A, where P is the original investment, r is the interest rate, t is the number of years, and n represents the number of times per year the money earns interest. Which graph could represent this investment over at least 50 years?

1) /
2) /
3) /
4) /

6Which equation has real, rational, and unequal roots?

1) /
2) /
3) /
4) /

7Which statement is true about the graphs of f and g shown below?

1) / f is a relation and g is a function.
2) / f is a function and g is a relation.
3) / Both f and g are functions.
4) / Neither f nor g is a function.

8The common ratio of the sequence is

1) /
2) /
3) /
4) /

9How many different ways can teams of four members be formed from a class of 20 students?

1) / 5
2) / 80
3) / 4,845
4) / 116,280

10If , what is the value of ?

1) /
2) /
3) /
4) /

11When factored completely, the expression is equivalent to

1) /
2) /
3) /
4) /

12When is multiplied by its conjugate, the result is

1) /
2) /
3) / 5
4) / 13

13A circle with center O and passing through the origin is graphed below.

What is the equation of circle O?

1) /
2) /
3) /
4) /

14Which expression is equivalent to ?

1) /
2) /
3) /
4) /

15Which trigonometric expression does not simplify to 1?

1) /
2) /
3) /
4) /

16What is the product of and ?

1) /
2) /
3) /
4) /

17What is the product of the roots of ?

1) /
2) /
3) /
4) /

18How many different 11-letter arrangements are possible using the letters in the word “ARRANGEMENT”?

1) / 2,494,800
2) / 4,989,600
3) / 19,958,400
4) / 39,916,800

19What is the third term in the expansion of ?

1) /
2) /
3) /
4) /

20Angle is in standard position and is a point on the terminal side of . What is the value of ?

1) /
2) /
3) / 0
4) / undefined

21The domain of is the set of all real numbers

1) / greater than 2
2) / less than 2
3) / except 2
4) / between and 2

22Which equation could be used to solve ?

1) /
2) /
3) /
4) /

23How many distinct triangles can be constructed if , side , and side ?

1) / one acute triangle
2) / one obtuse triangle
3) / two triangles
4) / none

24The expression is equivalent to

1) / 0
2) /
3) /
4) /

25The table below shows five numbers and their frequency of occurrence.

The interquartile range for these data is

1) / 7
2) / 5
3) / 7 to 12
4) / 6 to 13

26A wheel has a radius of 18 inches. Which distance, to the nearest inch, does the wheel travel when it rotates through an angle of radians?

1) / 45
2) / 23
3) / 13
4) / 11

27If , then equals

1) /
2) /
3) /
4) /

28If p and q vary inversely and p is 25 when q is 6, determine q when p is equal to 30.

29Express in simplest form:

30Solve algebraically for x, rounded to the nearest hundredth.

31Determine, to the nearest minute, the degree measure of an angle of radians.

32The probability of Ashley being the catcher in a softball game is . Calculate the exact probability that she will be the catcher in exactly five of the next six games.

33If x is a real number, express in simplest form.

34On a test that has a normal distribution of scores, a score of 57 falls one standard deviation below the mean, and a score of 81 is two standard deviations above the mean. Determine the mean score of this test.

35The area of a parallelogram is 594, and the lengths of its sides are 32 and 46. Determine, to the nearest tenth of a degree, the measure of the acute angle of the parallelogram.

36The table below shows the amount of a decaying radioactive substance that remained for selected years after 1990.

Write an exponential regression equation for this set of data, rounding all values to the nearest thousandth. Using this equation, determine the amount of the substance that remained in 2002, to the nearest integer.

37Use the recursive sequence defined below to express the next three terms as fractions reduced to lowest terms.

38The periodic graph below can be represented by the trigonometric equation where a, b, and c are real numbers.

State the values of a, b, and c, and write an equation for the graph.

39A homeowner wants to increase the size of a rectangular deck that now measures 14 feet by 22 feet. The building code allows for a deck to have a maximum area of 800 square feet. If the length and width are increased by the same number of feet, find the maximum number of whole feet each dimension can be increased and not exceed the building code. [Only an algebraic solution can receive full credit.]

Algebra 2/Trigonometry Regents Exam 0115

1ANS:2PTS:2REF:011501a2STA:A2.A.73

TOP:Law of CosinesKEY:side, without calculator

2ANS:2PTS:2REF:011502a2STA:A2.A.52

TOP:Identifying the Equation of a Graph

3ANS:3PTS:2REF:011503a2STA:A2.A.28

TOP:Logarithmic EquationsKEY:basic

4ANS:4PTS:2REF:011504a2STA:A2.A.34

TOP:Sigma Notation

5ANS:1PTS:2REF:011505a2STA:A2.A.53

TOP:Graphing Exponential Functions

6ANS:2

PTS:2REF:011506a2STA:A2.A.2TOP:Using the Discriminant

7ANS:2PTS:2REF:011507a2STA:A2.A.38

TOP:Defining FunctionsKEY:graphs

8ANS:1

PTS:2REF:011508a2STA:A2.A.31TOP:Sequences

9ANS:3

PTS:2REF:011509a2STA:A2.S.11TOP:Combinations

10ANS:3

PTS:2REF:011510a2STA:A2.A.77TOP:Double Angle Identities

KEY:evaluating

11ANS:2

PTS:2REF:011511a2STA:A2.A.7TOP:Factoring by Grouping

12ANS:4

PTS:2REF:011512a2STA:A2.N.9

TOP:Multiplication and Division of Complex Numbers

13ANS:4PTS:2REF:011513a2STA:A2.A.49

TOP:Equations of Circles

14ANS:2

PTS:2REF:011514a2STA:A2.A.9TOP:Negative Exponents

15ANS:3

PTS:2REF:011515a2STA:A2.A.67TOP:Proving Trigonometric Identities

16ANS:1

PTS:2REF:011516a2STA:A2.N.2TOP:Operations with Radicals

17ANS:3

PTS:2REF:011517a2STA:A2.A.20TOP:Roots of Quadratics

18ANS:1

PTS:2REF:011518a2STA:A2.S.10TOP:Permutations

19ANS:1

PTS:2REF:011519a2STA:A2.A.36TOP:Binomial Expansions

20ANS:2

PTS:2REF:011520a2STA:A2.A.62TOP:Determining Trigonometric Functions

21ANS:2PTS:2REF:011521a2STA:A2.A.39

TOP:Domain and RangeKEY:real domain

22ANS:3

PTS:2REF:011522a2STA:A2.A.23TOP:Solving Rationals

KEY:irrational and complex solutions

23ANS:4

PTS:2REF:011523a2STA:A2.A.75TOP:Law of Sines - The Ambiguous Case

24ANS:4

PTS:2REF:011524a2STA:A2.N.3TOP:Operations with Polynomials

25ANS:2

PTS:2REF:011525a2STA:A2.S.4TOP:Dispersion

KEY:range, quartiles, interquartile range, variance

26ANS:2

PTS:2REF:011526a2STA:A2.A.61TOP:Arc Length

KEY:arc length

27ANS:4

PTS:2REF:011527a2STA:A2.A.41TOP:Functional Notation

28ANS:

PTS:2REF:011528a2STA:A2.A.5TOP:Inverse Variation

29ANS:

PTS:2REF:011529a2STA:A2.A.16TOP:Multiplication and Division of Rationals

KEY:division

30ANS:

PTS:2REF:011530a2STA:A2.A.27TOP:Exponential Equations

KEY:without common base

31ANS:

PTS:2REF:011531a2STA:A2.M.2TOP:Radian Measure

KEY:degrees

32ANS:

PTS:2REF:011532a2STA:A2.S.15TOP:Binomial Probability

KEY:exactly

33ANS:

PTS:2REF:011533a2STA:A2.N.9

TOP:Multiplication and Division of Complex Numbers

34ANS:

PTS:2REF:011534a2STA:A2.S.5TOP:Normal Distributions

KEY:mean and standard deviation

35ANS:

PTS:2REF:011535a2STA:A2.A.74TOP:Using Trigonometry to Find Area

KEY:Parallelograms

36ANS:

PTS:4REF:011536a2STA:A2.S.7TOP:Exponential Regression

37ANS:

PTS:4REF:011537a2STA:A2.A.33TOP:Recursive Sequences

38ANS:

.

PTS:2REF:011538a2STA:A2.A.72

TOP:Identifying the Equation of a Trigonometric Graph

39ANS:

10 feet increase.

PTS:6REF:011539a2STA:A2.A.25TOP:Quadratics with Irrational Solutions